In square ABCE shown below, D is the midpoint of CE. Which of the following is the ratio of the area of ABE to the area of ADB?
F. 1:1
G. 1:2
H. 1:3
J. 1:4
k.1:8
To find the ratio of the area of triangle ABE to the area of triangle ADB, we need to first find the area of both triangles.
Since D is the midpoint of CE, we know that triangle ADB is half the area of triangle ACE.
Let's say the area of triangle ACE is represented by x. Then the area of triangle ADB is x/2.
Now, triangle ABE is half the area of triangle ACE as well because triangle ABE shares the same height as triangle ADB (height from A to CE is the same as the height from A to BD).
Therefore, the area of triangle ABE would also be x/2.
So, the ratio of the area of triangle ABE to the area of triangle ADB is (x/2)/(x/2) = 1:1.
Therefore, the correct answer is F. 1:1.